## Greatest Common Divisor

In mathematics, the **greatest common divisor** (**gcd**), also known as the **greatest common factor** (**gcf**), or **highest common factor** (**hcf**), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4.

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### Some articles on greatest common divisor:

Common-mode Signal

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**Common**-mode signal is the component of an analog signal which is present with one sign on all considered conductors ... In telecommunication,**common**-mode signal on a transmission line is known as longitudinal voltage ... where the signal is transferred with differential voltage use, the**common**-mode signal is called a half-sum of voltages When referenced to the local**common**or ground, a**common**...**Greatest Common Divisor**- The Gcd in Commutative Rings

... The notion of

**greatest common divisor**can more generally be defined for elements of an arbitrary commutative ring, although in general there need not exist one for ... in R, then an element d of R is called a

**common divisor**of a and b if it divides both a and b (that is, if there are elements x and y in R such that d·x = a and d·y = b) ... If d is a

**common divisor**of a and b, and every

**common divisor**of a and b divides d, then d is called a

**greatest common divisor**of a and b ...

Recursive Call - Recursive Programs - Recursive Procedures -

... The Euclidean algorithm, which computes the

**Greatest Common Divisor**... The Euclidean algorithm, which computes the

**greatest common divisor**of two integers, can be written recursively ... otherwise, return end gcd Recurrence relation for**greatest common divisor**, where expresses the remainder of Computing the recurrence relation for x = 27 ...**Greatest Common Divisor**Of Two Polynomials - General Definition

... A

**greatest common divisor**of p and q is a polynomial d that divides p and q and such that every

**common divisor**of p and q also divides d ... If F is a field and p and q are not both zero, d is a

**greatest common divisor**if and only if it divides both p and q and it has the

**greatest**degree among the ... The

**greatest common divisor**of p and q is usually denoted "gcd(p, q)" ...

**Greatest Common Divisor**Of Two Polynomials

... In algebra, the

**greatest common divisor**(frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that evenly divides each of the two original polynomials ... This concept is analogous to the

**greatest common divisor**of two integers ... Therefore, "

**greatest**" is meant for the relation of divisibility ...

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—Mark Twain [Samuel Langhorne Clemens] (1835–1910)

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